
TABLE OF CONTENTS 

CH 4
CH 8
CH 12 

CH 1 
ESSENTIALS OF GEOMETRY  


SAT 
TE 
11 
Undefined Terms  




12 
The Real Numbers and Their Properties  


ACY 

13 
Definitions, Lines, and Line Segments  




14 
Midpoints and Bisectors  




15 
Rays and Angles  




16 
More Angle Definitions  




17 
Triangles  


ACY 

CH 2 
LOGIC  


SAT 
TE 
21 
Sentences, Statements, and Truth Values 
G.G.24 
ACY 

22 
Conjunctions 
G.G.25 


23 
Disjunctions 
ACY 

24 
Conditionals 


25 
Inverses, Converses, and Contrapositives 
G.G.26 


26 
Biconditionals 
G.G.25 


27 
The Laws of Logic  




28 
Drawing Conclusions  




CH 3 
PROVING STATEMENTS IN GEOMETRY  


SAT 
TE 
31 
Inductive Reasoning  




32 
Definitions as Biconditionals  


ACY 

33 
Deductive Reasoning  




34 
Direct and Indirect Proofs 
G.G.27 


35 
Postulates, Theorems, and Proof 


36 
The Substitution Postulate 
ACY 

37 
The Addition and Subtraction Postulates 


38 
The Multiplication and Division Postulates 



CH 4 
CONGRUENCE OF LINE SEGMENTS, ANGLES, AND
TRIANGLES  


SAT 
TE 
41 
Postulates of Lines, Line Segments, and Angles 
G.G.27
G.G.28
G.G.29 
ACY 

42 
Using Postulates and Definitions in Proofs 


43 
Proving Theorems About Angles 


44 
Congruent Polygons and Corresponding Parts 


45 
Proving Triangles Congruent Using Side, Angle, Side 


46 
Proving Triangles Congruent Using Angle, Side, Angle 


47 
Proving Triangles Congruent Using Side, Side, Side 
ACY 

CH 5 
CONGRUENCE BASED ON TRIANGLES 

SAT 
TE 
51 
Line Segments Associated with Triangles 
G.G.21
G.G.27
G.G.28
G.G.29
G.G.31
G.G.42 


52 
Using Congruent Triangles to Prove Line Segments
Congruent and Angles Congruent 


53 
Isosceles and Equilateral Triangles 
ACY 

54 
Using Two Pairs of Congruent Triangles 


55 
Proving Overlapping Triangles Congruent 


56 
Perpendicular Bisector of a Line Segment 


57 
Basic Constructions 
G.G.17
G.G.18
G.G.19
G.G.20 
ACY 

CH 6 
TRANSFORMATIONS AND THE COORDINATE PLANE  


SAT 
TE 
61 
The Coordinates of a Point in a Plane  




62 
Line Reflections 
G.G.54
G.G.55
G.G.56
G.G.61 


63 
Line Reflections in the Coordinate Plane 
ACY 

64 
Point Reflections in the Coordinate Plane 


65 
Translations in the Coordinate Plane 


66 
Rotations in the Coordinate Plane 
ACY 

67 
Glide Reflections 
ACY 

68 
Dilations in the Coordinate Plane 
G.G.58
G.G.59
G.G.61 


69 
Transformations as Functions  




CH 7 
GEOMETRIC INEQUALITIES 



SAT 
TE 
71 
Basic Inequality Postulates  


ACY 

72 
Inequality Postulates Involving Addition and
Subtraction  




73 
Inequality Postulates Involving Multiplication and
Division  




74 
An Inequality Involving the Lengths of the Sides of
a Triangle 
G.G.33 
ACY 

75 
An Inequality Involving an Exterior Angle of a
Triangle 
G.G.32 


76 
Inequalities Involving Sides and Angles of a
Triangle 
G.G.34 



CH 8 
SLOPES AND EQUATIONS OF LINES  


SAT 
TE 
81 
The Slope of a Line  




82 
The Equation of a Line  


ACY 

83 
Midpoint of a Line Segment  




84 
The Slopes of Perpendicular Lines  




85 
Coordinate Proof  


ACY 

86 
Concurrence of the Altitudes of a Triangle 
G.G.21 


CH 9 
PARALLEL LINES  


SAT 
TE 
91 
Proving Lines Parallel 
G.G.35 


92 
Properties of Parallel Lines 


93 
Parallel Lines in the Coordinate Plane  




94 
The Sum of the Measures of the Angles of a Triangle 
G.G.30
G.G.32 


95 
Proving Triangles Congruent by Angle, Angle, Side  




96 
The Converse of the Isosceles Triangle Theorem 
G.G.31 


97 
Proving Right Triangles Congruent by Hypotenuse, Leg 
G.G.21 


98 
Interior and Exterior Angles of Polygons 
G.G.36
G.G.37 
ACY 

CH 10 
QUADRILATERALS 
G.G.38
G.G.39
G.G.41 
SAT 
TE 
101 
The General Quadrilateral 


102 
The Parallelogram 
ACY 

103 
Proving That a Quadrilateral Is a Parallelogram 
ACY 

104 
The Rectangle 


105 
The Rhombus 


106 
The Square 
ACY 

107 
The Trapezoid 
G.G.40
G.G.41 


108 
Areas of Polygons  




CH 11 
THE GEOMETRY OF THREE DIMENSIONS  


SAT 
TE 
111 
Points, Lines, and Planes 
G.G.1
G.G.2
G.G.3
G.G.4
G.G.7
G.G.8
G.G.9 


112 
Perpendicular Lines and Planes 


113 
Parallel Lines and Planes 


114 
Surface Area of a Prism 
G.G.10 


115 
Volume of a Prism 
G.G.11
G.G.12 


116 
Pyramids 
G.G.13 


117 
Cylinders 
G.G.14 


118 
Cones 
G.G.15 


119 
Spheres 
G.G.16 
ACY 


CH 12 
RATIO, PROPORTION, AND SIMILARITY  


SAT 
TE 
121 
Ratio and Proportion  




122 
Proportions Involving Line Segments  




123 
Similar Polygons  


ACY 

124 
Proving Triangles Similar 
G.G.44
G.G.45
G.G.46 


125 
Dilations  




126 
Proportional Relations Among Segments Related to
Triangles  




127 
Concurrence of the Medians of a Triangle 
G.G.21
G.G.43 
ACY 

128 
Proportions in a Right Triangle 
G.G.47 


129 
Pythagorean Theorem 
G.G.48 


1210 
The Distance Formula  




CH 13 
GEOMETRY OF THE CIRCLE  


SAT 
TE 
131 
Arcs and Angles  




132 
Arcs and Chords 
G.G.49 


133 
Inscribed Angles and Their Measures 
G.G.51 
ACY 

134 
Tangents and Secants 
G.G.50 


135 
Angles Formed by Tangents, Chords, and Secants 
G.G.51 


136 
Measures of Tangent Segments, Chords, and Secant
Segments 
G.G.53 
ACY 

137 
Circles in the Coordinate Plane  




138 
Tangents and Secants in the Coordinate Plane  




CH 14 
LOCUS AND CONSTRUCTION  


SAT 
TE 
141 
Constructing Parallel Lines 
G.G.19 


142 
The Meaning of Locus 
G.G.22
G.G.23 


143 
Five Fundamental Loci 


144 
Points at a Fixed Distance in Coordinate Geometry 


145 
Equidistant Lines in Coordinate Geometry 


146 
Points Equidistant from a Point and a Line 
ACY 


 





INDEX  



